Q2E - University Physics with Modern Physics

Question

In Fig. E5.2 each of the suspended blocks has weight w. The pulleys are frictionless, and the ropes have negligible weight. In each case, draw a free-body diagram and calculate the tension T in the rope in terms of w.

Step-by-Step Solution

Answer

(a) The tension in the rope is w .

(b) The tension in the chain is w .

(c) The tension in the rope is w .

Step 1: Tension in rope

Given Data:

• The weight of each block for all cases is $w$ .

 

The tension in each rope for all the cases are same because the weight attached to each rope is the same.

Determine the tension in the rope (a)

The FBD of the block in case (a) is given below:

 

The equation for the vertical equilibrium of the weight is given as:

 $$\begin{gathered} T-w=0 \\ T=0 \end{gathered}$$ 

Here   is the tension in the rope and$w$ is the weight attached to the rope.

Therefore, the tension in the rope is$w$.

 

(b)

The FBD of the block in case (b) is given below

The equation for the vertical equilibrium of the weight is given as:

$$\begin{gathered} T-w=0 \\ T=0 \end{gathered}$$  

Therefore, the tension in the rope is $w$ .

 

(c)

The FBD of the block is given below

The equation for the vertical equilibrium of the weight is given as:

 $$\begin{gathered} T-w=0 \\ T=0 \end{gathered}$$ 

Therefore, the tension in the rope is$w$.